New concepts in meshless methods

By Satya N. Atluri, T. Zhu. 2000

248 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/cb68eb8a171d625ce7be6e65db6f7da2c66a736c

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A meshless method using the radial basis functions for numerical solution of the regularized long wave equation (2010, background): “The interested reader can see [16–22] formore investigations in RBFs.”
Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems (2005, methodology): “The success of the MLPG method has been reported in solving fracture mechanics problems [10], beam and plate bending problems [11], three dimensional elasto-static and -dynamic problems [12,13] and some fluid dynamic problems such as steady flow around a cylinder [8], steady convection and diffusion”
Quadrature for meshless methods (2008, background): “In spite of its importance, only a few papers ([1],[2],[3],[4],[5],[6],[7]) address it, and these concentrate mainly on implementational aspects.”
Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry (2003, methodology): “In fact, since the BNM still requires meshes in its numerical integration, it is not a truly meshless scheme like those MLS-based meshless FEMs [4,7].”
A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids (2001, methodology): “For example, the MLPG method has been used for two-dimensional elasto-statics (Atluri and Zhu 2000b) and one-dimensio al 4th order thin beam static analysis (Atluri et al. 1999a).”
Comparisons of two meshfree local point interpolation methods for structural analyses (2002, methodology): “Te MLPG method is proposed and developed by Atluri and his co-workers ( Atluri and Zhu, 1998, 2000; Atluri et al., 1999).”
Elasto‐plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming (2002, methodology): “[5] (DEM), element-free Galerkin [6–8] (EFG), reproducing kernel particle method [9–13] (RKPM), HP clouds [14], meshless local Petrov–Galerkin (MLPG) approach [15] and free mesh method [16] (FMM).”
The Generalized Interpolation Material Point Method (2004, methodology): “…use of both grid and particle basis functions to represent test functions and trial functions, respectively, is a Petrov–Galerkin method, [Johnson (1987)], and therefore more akin to some of the meshless methods (in particular [Demkowicz and Oden (1986); Atluri and Zhu (2000)]) than the FEM.”